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प्रश्न
State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air.
The refractive indices of glass and water with respect to vacuum are 3/2 and 4/3 respectively. If the speed of light in glass is 2 × 108m/s, find the speed of light in (i) vacuum, (ii) water.
उत्तर
The law of refraction that defines the refractive index of a medium with respect to the other is given by first law of refraction known as Snell’s law.
First law of refraction
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
This is known as Snell’s law. Mathematically, it can be given as follows:
`sini/sinr="constant"=` \[^aμ_b\]
Here, \[^aμ_b\] is the relative refractive index of medium b with respect to medium a. Consider a ray of light travelling from medium B into medium A. Let v1 be the speed of light in medium A and v2 be the speed of light in medium B. Then the refractive index of medium A with respect to medium B is given by
`n_(AB)=v_2/v_1`
If one medium is vacuum or air then the constant is named as absolute refractive index of the medium.
Let, absolute refractive index of glass, `n_g=3/2`
Absoluterefractive index of water, `n_w=4/3`
Speed of light in glass, vg = 2 × 108 m/s
(i) Speed of light in vacuum
`n_g=c/v_g`
`c=n_gxxv_g=3/2xx2xx10^8=3xx10^8 `m/s
(ii) Speed of light in water,
`n_w=c/v_w`
`v_w=c/n_w=(3xx10^8)/((4/3))=2.25xx10^8` m/s
संबंधित प्रश्न
The refractive index of diamond is 2.42. What is the meaning of this statement?
A ray of light travelling in air goes into water. The angle of refraction will be:
(a) 90°
(b) smaller than the angle of incidence
(c) equal to the angle of incidence
(d) greater than the angle of incidence
What name is given to the ratio of sine of angle of incidence to the sine of angle of refraction?
The refractive indexes of four substances P, Q, R and S are 1.77, 1.50, 2.42 and 1.31 respectively. When light travelling in air is incident on these substances at equal angles, the angle of refraction will be the maximum in:
(a) substance P
(b) substance Q
(c) substance R
(d) substance S
State Snell’s law of refraction of light. Write an expression to relate refractive index of a medium with speed of light in vacuum.
The refractive index of a medium ‘a’ with respect to medium ‘b’ is 2/3 and the refractive index of medium ‘b’ with respect to medium ‘c’ is 4/3. Find the refractive index of medium ‘c’ with respect to medium ‘a’.
Prove the statement.
If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.
If the absolute refractive index of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?
Define the refractive index of a medium.
Noor, a young student, was trying to demonstrate some properties of light in her Science project work. She kept ‘X’ inside the box (as shown in the figure) and with the help of a laser pointer made light rays pass through the holes on one side of the box. She had a small butter-paper screen to see the spots of light being cast as they emerged.
If the object inside the box was made of a material with a refractive index less than 1.5 then the ______.
Match the pair:
| Group 'A' | Group 'B' | |
| Substance | Refractive index | |
| Air | (a) | 1.33 |
| (b) | 1.46 | |
| (c) | 1.0003 |
